Electrostatic forces 568 INDEX

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

Dielectric constant A value that serves as an index of the ability of a substance to resist the transmission of an electrostatic force from one charged body to another the lower the value, the greater the resistance. Diels-Alder reation A reaction involving the addition of an ethylenic double bond to a conjugated diene. 

J. Bjerrum (1926) first developed the theory of ion association. He introduced the concept of a certain critical distance between the cation and the anion at which the electrostatic attractive force is balanced by the mean force corresponding to thermal motion. The energy of the ion is at a minimum at this distance. The method of calculation is analogous to that of Debye and Hiickel in the theory of activity coefficients (see Section 1.3.1). The probability Pt dr has to be found for the ith ion species to be present in a volume element in the shape of a spherical shell with thickness dr at a sufficiently small distance r from the central ion (index k). 

In the majority of continuum solvation models incorporating a surface-tension approach to estimating the non-electrostatic solvation components, the index k in Eq. (11.22) runs over a list of atom types, and die user assigns the appropriate type to each atom of the solute. This is particularly straightforward for MM models, like the Generalized Bom/Surface Area (GB/SA) model (Still el al. 1990 see also Best, Merz, and Reynolds 1997), since atom types are already intrinsic to the force field approach. This same formalism has been combined with the CHARMM and Cornell et al. force fields (see Table 2.1) to define GB models for proteins and nucleic acids (Dominy and Brooks 1999 Jayaram, Sprous, and Beveridge 1998). Considering this approach applied within the QM arena, the MST-ST models of Orozco and Luque have been the most extensively developed (see, for instance, Curutchet, Orozco, and Luque 2001). 

Two classical tools, the intermolecular stretching force constants of H-bonded complexes and the molecular electrostatic potential, were used to develop a nucleophilicity index, which was validated against kinetic data recorded for the aminolysis of S-methyl 2,4-dinitrophenylthiocarbamate.51 Aminolysis of iV-phenylthionocarbamates by ben-zylamines in MeCN proceeded by a stepwise mechanism in which the rate-determining step was the breakdown of the zwitterionic tetrahedral intermediate.52... 

Across real surfaces and interfaces, the dielectric response varies smoothly with location. For a planar interface normal to a direction z, we can speak of a continuously changing s(z). More pertinent to the interaction of bodies in solutions, solutes will distribute nonuniformly in the vicinity of a material interface. If that interface is charged and the medium is a salt solution, then positive and negative ions will be pushed and pulled into the different distributions of an electrostatic double layer. We know that solutes visibly change the index of refraction that determines the optical-frequency contribution to the charge-fluctuation force. The nonuniform distribution of solutes thereby creates a non-uniform e(z) near the interfaces of a solution with suspended colloids or macromolecules. Conversely, the distribution of solutes can be expected to be perturbed by the very charge-fluctuation forces that they perturb through an e(z).5... 

In addition to the repulsive electrostatic interactions, two isolated identical particles immersed in a solvent of different index of refraction, experience an attractive interaction, namely, the van der Walls or dispersion forces, which arise from the induced dipolar interactions between the molecules constituting the two particles. This interaction depends on the geometry (the shape of the particles) and on the material of which the particles are made of. For two spherical particles, the van der Waals interparticle potential uyj(r) is given by... 

Perhaps the more important questions raised by Rule 5, as Burdett and McLarnan (1984) point out, concern the extent to which it really is borne out by observation. For example, Baur et al. (1983) have developed a numerical index for the degree of parsimony in a crystal structure and have shown that, using this measure, many crystal structures are not parsimonious but lavish in their use of different local environments. Also, the dominance of short-range forces is by no means obvious when ordered structures with extremely large unit cells are observed (e.g., a c dimension of 1500 A in some SiC polytypes Shaffer, 1969). The explanation of such structures poses problems for electrostatic as well as covalent models. 

At mtermediate electrolyte concentrations ( 10 mol dm" ) and at low volume fractions of the dispersed phase, the charged particles occupy random positions in the system and undergo continuous Brownian motion with transient repulsive contacts when the particles approach each other. The range of the electrostatic repulsive forces is represented by the dashed circle in Fig. 1. which implies that when a similar circle on another particle overlaps with it on a collision trajectory, a transient electrostatic repulsion occurs and the particles move out of range. With most latices the particles. have a real refractive index and their visual appearance is milky white. 

The natural process of exchanged diffusion of the monomer-diffuser into the gel-polymer matrix with space-bonded structure was considered above. In [43, 44], the method of forced diffusion of monomer with a given refractive index and with a definite dipole moment to the matrix from solid linear polymer, imder the influence of an electrostatic field with a given... 

There are a number of interaction forces, which can exist between particles—attractive van der Waals, repulsive electrostatic, structural and solvation forces, forces due to adsorbed and non-adsorbing polymer etc. These forces can be manipulated by a variety of different means—by adding salt to screen the charge on the particles, to index match the solvent and particles to screen van der Waals interactions and changing the solvency to affect the state of the adsorbed polymer to name a few. The chemical sensitivity of these interactions becomes particularly important when dealing with sub-100 nm particles or for situations where particles are held at separations on the order of a few nanometers. In both cases, the granularity of the continuous phase and chemical details of the interactions of the species in solution with the solid surface begin to dominate interactions. If conditions where the particles are held at small separations are of interest, these interactions must be characterized, as they cannot at present, be predicted. 

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